In the cube of side $a$ shown in the figure, the vector from the central point of the face $A B O D$

Question

In the cube of side $a$ shown in the figure, the vector from the central point of the face $A B O D$ to the central point of the face $B E F O$ will be

Professor PC Thomas Classes · Answer

(b) : The position vectors for points $G$ and $H$ are $\left(\frac{a}{2} \hat{k}+\frac{a}{2} \hat{i}ight)$ and $\left(\frac{a}{2} \hat{j}+\frac{a}{2} \hat{k}ight)$ respectively. So, the displacement vector from $G$ to $H$ is  \ $ \overrightarrow{O H}-\overrightarrow{O G}=\frac{a}{2}(\hat{k}+\hat{j}-\hat{k}-\hat{i})=\frac{a}{2}(\hat{j}-\hat{i}) $